The Focused Information Criterion for Logistic Time Series Regression Models Under Locally Biased Estimating Functions

Abstract

Statistical modeling of biomedical data arising from the cytologic samples collected during cancer trials often involves the analysis of binary time series responses indicating the status of the samples being benign or malignant. The model selection problems pertaining to such data involve exploring the Markovian dependence of the status of the cytologic samples collected in a timely manner on the potential covariates of the malignancy measured during each phase of the trial. In the present paper, we propose the focused information criterion (FIC) that facilitates the simultaneous selection of the order of the binary autoregressive response and a subset of covariates in logistic time series regression models. The FIC attempts to select the subset of covariates that minimizes the mean squared error in estimating a certain focus function of interest under the potential model misspecification. The focus function is chosen so as to adequately represent the purpose of statistical modeling for the concerned data. We derive the general expressions for the FIC using quasi-maximum likelihood estimators when the quasi-likelihood estimating functions are locally biased. In terms of minimizing the estimated mean squared error of the focus function, our FIC is seen to outperform the traditional FIC that ignores the bias in the underlying estimating functions induced by the potential model misspecification.